Program: CORMAP
Purpose: Check whether there is a correlation between two maps
Category: ANALYSIS, CALCULATION
File: cormap.c
Author: M. Vogelaar
Keywords:
INSET= Give set, subsets:
Maximum number of subsets is 2048.
BOX= Give box: [entire subset]
RANGE= Give range of levels to include in calculation: [all]
Input consists of two values. The first value may
be greater than the second. See the description
for the correct use of this keyword.
INSET2= Give set, subsets:
Number of subsets and subset dimension must be equal
to INSET= The size of INSET2= must be greater than
or equal to the size of BOX= otherwise a new set will be
asked.
BOX2= Give box in ..... [defaults by program]
The size of the second box must be equal to
the size of the first box.
If the edges of BOX= are contained within INSET2=, then
the defaults are these edges, else the default are the
maximum sizes of BOX=
RANGE2= Give range of levels to include in calculation: [all]
Range of levels for second (sub)set.
GRDEVICE= Plot device: [List of devices]
Destination of plot, Screen or Hardcopy.
PGMOSAIC= View surface sub divisions in x,y: [1,1]
View surface can contain a number of plots in
in X and Y direction (mosaic). Default is 1 plot in
both X- and Y direction.
PGPAPER= Give width(cm), aspect ratio: [calc, calc]
Aspect ratio is height/width.
PGBOX= Corners of box Xl,Yl,Xh,Yh: [default by application]
It is possible to overrule the calculated
PGPLOT box size with PGBOX=. The coordinates (x,y) of
the lower point are given first.
PGCOLOR= Give color 1..15: [1]
See description for the available colors.
PGWIDTH= Give line width 1..21: [1]
PGHEIGHT= Give character height: [1.0]
PGFONT= Give font 1..4: [2]
Description: CORMAP makes a diagram with pixel values of two
(sub)sets plotted against each other. The pixels
have data ranges as given in RANGE= and RANGE2=
Furthermore, it
calculates the regression lines y=ax+b and x=cy+d, the
deviations from these lines and the linear correlation
coefficient r. If r = 1 or r = -1, there is perfect
positive resp. negative correlation. If r = 0, there is
total absence of correlation.
The square root of the variance is calculated, where
the variance is given by:
2 1 2
S = ----- SUM[ (Yi - a - b*Xi) ]
n - 2
If n is the number of valid data pairs in the regression,
the significance of r is the probability Pc(r,n) that
the data points could represent a sample from an
uncorrelated parent population:
Pc(r,n) < 5% is significant.
Pc(r,n) < 1% is highly significant.
Pc(r,n) < 0.1% is very highly significant.
In most cases with large n, this probability is so
small, that 0(%) is printed.
The applied statistic t = r * sqrt( n-2 / 1-r**2 ) is
distributed in the case of the null-hypothesis (of no
correlation) like Student's t-distribution with
v = n-2 degrees of freedom.
The two sided significance level is given by Pc(r,n).
References:
-Kreyszig, E., Introductory Mathematical Statistics
Chapter 17, 18.
-Press, H. et al, Numerical Recipes, Chapter 14.
-Bevington, P., Data Reduction and Error Analysis
for the Physical Sciences, Chapter 7.
-Ractliffe, J., Elements of Mathematical Statistics
Chapter 16.
The number of input subsets and the dimension of the
subsets must be equal. The box sizes must be equal.
Blanks in either one of the subsets will not be
plotted and are not taken into calculation.
Examples of the use of the RANGE= keyword:
RANGE=2, 5
(IF 2blank)
RANGE=5, 2
(IF 2blank ELSE use this value)
At the RANGE= keyword, the values -INF and INF can
be input also. These values represent the minimum
and maximum values of the current system.
RANGE=5, INF
(IF value>5 THEN use this value ELSE value==>blank)
Color indices for PGCOLOR=
0 Background
1 Default (Black if background is white)
2 Red
3 Green
4 Blue
5 Cyan
6 Magenta
7 Yellow
8 Orange
7 Yellow
8 Orange
9 Green + Yellow
10 Green + Cyan
11 Blue + Cyan
12 Blue + Magenta
13 Red + Magenta
14 Dark Gray
15 Light Gray
16-255 Undefined
Available fonts for PGFONT=
1 single stroke "normal" font
2 roman font
3 italic font
4 script font
Notes:
Example:
cormap
CORMAP INSET=hi1277 1
CORMAP BOX=
CORMAP INSET2=hi1277 2
CORMAP BOX2=
CORMAP GRDEVICE=g
Statistics
==========
Data points diagram : n = 100
Regression Y on X : Y = +0.9804 (+/-0.0357) X + -2.1644 (+/-0.3035)
Regression X on Y : X = +0.9026 (+/-0.0328) Y + +1.9823 (+/-0.2978)
Linear corr. coeff. : r = 0.940727
Significance of r : Pc(r,n) = 0.0(%)
Pc(r,n) < 5% is significant.
Pc(r,n) < 1% is highly significant.
Pc(r,n) < 0.1% is very highly significant.
CORMAP +++ FINISHED +++
Updates: May 7, 1992: VOG, Document created.
Jul 27, 1999: VOG, Increased length of message for
longer box text.